Timing Response-Based Clock Frequency Offset Estimation Method For Industrial Wireless Sensor Network

ABSTRACT

The present invention relates to a method for estimating clock frequency offsets of industrial wireless sensor networks based on timing response. In the method, a data packet is sent from a node to be synchronized to a reference node. After the reference node receives the data packet, it replies an acknowledgement after a timing response interval, which is mapped according to a sequence number of the data packet. After communication and interaction for multiple times, a relative frequency offset and a fixed delay between node clocks can be estimated by the node to be synchronized without exchanging timestamp information. The present invention does not need to receive or send messages specially used for time synchronization parameter estimation, which realizes a long-term tracking of clock frequency offset with a low computation cost and reduces communication overhead and energy consumption.

FIELD OF INVENTION

The present invention belongs to the technical field of wireless sensornetworks, which relates to a method for estimating timing response clockfrequency offsets applicable to industrial wireless sensor networks.

BACKGROUND ART OF THE INVENTION

A wireless sensor network is composed of a plurality of cheap and tinysensor nodes which are distributed in space and have limited calculationability, storage capacity and energy. All nodes operate on their ownindependent clocks. Because of the characteristics such as flexibledeployment and low cost, wireless sensor networks have been widely usedin many fields such as industry. Most of the traditional industrialnetworks adopt a wired connection mode, which limits the deploymentflexibility and the intelligent control of an industrial process. Basedon the advantages of wireless sensor networks, industrial wirelesssensor networks emerge as the industries require. Wireless micro sensornodes are deployed on many industrial field devices and are responsiblefor collecting industrial environmental data and industrial processdata, and a large number of sensor nodes operate cooperatively torealize a high-efficient, flexible and intelligent industrial process. Acomplex industrial field environment leads to high requirements forreliability, real-time performance and low power consumption ofindustrial wireless sensor networks. Currently, ISA100.11a and otherwireless sensor network standards specially used for industrial fieldenvironment have been established.

Time synchronization technology is an important supporting technologyfor the application of the industrial wireless sensor networks anddifferent nodes are required to operate on a common time scale in thepractical application of the industrial wireless sensor networks.Consider that clock frequency offset is a main factor causingsynchronization errors among the nodes, therefore it is important forthe industrial wireless sensor network to obtain clock frequency offsetparameters of the nodes. The existing methods for estimating clockfrequency offsets usually need dedicated synchronization messages andtimestamp information exchange during transmission, thereby causingrelatively large synchronization overhead.

Aiming at the above problems, the present invention provides a relativeclock frequency estimation method based on timing response forindustrial wireless sensor networks with a time slot mechanism. Byembedding the implementation of frequency offset estimation into thesending and acknowledgement (ACK) processes of ordinary data packets,long-term tracking of frequency offsets can be realized withouttransmitting special time synchronization messages and timestampinformation. Moreover, the possibility of timestamp attack is avoided,synchronization overhead of resource-limited industrial wireless sensornetworks is reduced, thus improving the synchronization safety.

DISCLOSURE OF THE INVENTION

In view of this, the purpose of the present invention is to provide amethod for estimating clock frequency offsets of industrial wirelesssensor networks based on timing response, which does not need dedicateddata frames to exchange timestamp information between synchronizationnodes. The nodes can realize long-term smooth tracking of clocksynchronization frequency offsets during transmission of network datapackets, and more accurate clock frequency offsets are obtained with alow cost. Therefore, the present invention reduces the number oftransmission messages in the network and the communication overhead ofresource-limited nodes. In addition, this present invention avoids thepotential possibility of timestamp message attack during timesynchronization exchange, and thus improves the safety and reliabilityof the network.

To achieve the above purpose, the present invention provides thefollowing technical solution:

A method for estimating clock frequency offsets of industrial wirelesssensor networks based on timing response, which does not need additionalcommunication bandwidth specially used for clock synchronizationparameter estimation to transmit the message specially used for timesynchronization in a wireless sensor network, and does not needtimestamp exchange between nodes. When an arbitrary node S to besynchronized in the network needs to realize synchronization with areference node R, two-way communication between the nodes is carried outin a communication mode of one-way data packet+ACK.

A time synchronization algorithm is performed along with data sendingand receiving of a sending node S. It is assumed that the node S sends adata packet to the reference node R at its local time T_(1,i) ^((s)),the reference node R receives the data packet after a period of time,the period of time is mainly influenced by a fixed time delay d₁ and arandom time delay X_(i) during data packet transmission. The referencenode R receives a message the data packet message sent by the node S atits local time T_(2,i) ^((R)), and returns an acknowledgement message atits local time T_(3,i) ^((R)) after a timing response interval w_(i).Here, timing response intervals corresponding to different data packetsare calculated in a mode of sequence numbers modulo i(i≥2) according todifferent sequence numbers Seq of the data packets in the network.Specifically, when the sequence number Seq % i=0, ACK is returned aftera timing response interval w₁; when the sequence number Seq %1=1, ACK isreturned after a timing response interval w₂; when the sequence numberSeq % i=2, ACK is returned after a timing response interval w₃; . . . ;when Seq % i=i−2, ACK is returned after a timing response intervalw_(i-1); and when Seq % i=i−1, ACK is returned after a timing responseinterval w_(i), (both a receiver and a sender know correspondingcalculation rules in advance, and wait according to the rules). At thetime T_(3,i) ^((R)), an ACK message is returned from the reference nodeR to the node S, and a time T_(4,i) ^((S)) when a response message isreceived is recorded by the node S. It should be noted that in thisprocess, the timestamp information of each sending or receiving time isnot carried in exchanged data frames. The above process is repeated.After N times of message exchange, the sending node S can obtain a groupof local timestamps {T_(1,i) ^((S)), T_(4,i) ^((S))}_(i=1) ^(N), andsimilarly, the node R can obtain a group of local timestamps {T_(2,i)^((R)), T_(3,i) ^((R))}_(i=1) ^(N). Combined with the different timingresponse intervals w_(i) of the node R, a frequency offset between thenodes and the fixed delay during transmission can be estimated by astatistical signal processing method.

The method for estimating clock frequency offsets specifically comprisesthe following steps:

S1: the estimation of clock frequency offset is performed along withdata packet sending and receiving of the nodes, assuming that the node Sto be synchronized sends a data packet to the reference node R at alocal time T_(1,i) ^((S)), and records the sending time T_(1,i) ^((S));S2: as crystal oscillators of the node R and the node S have differentfrequencies, if f_(R) represents a crystal oscillator frequency of thenode R, and f_(S) represents a crystal oscillator frequency of the nodeS, the reference node R records a local time T_(2,i) ^((R)) whenreceiving a data frame sent by the node S; as influenced by a fixeddelay d₁ during data packet transmission and a random delay X_(i) in anuplink, it can be obtained that

T _(2,i) ^((R)) =α×T _(1,i) ^((S))+θ_(t0)+α×(d ₁ +X _(i))

wherein

$\alpha = \frac{f_{R}}{f_{S}}$

represents clock frequency offset of the node S relative to the node R,θ_(t) ₀ represents initial phase offset between the nodes, X_(i),represents an independent and identically distributed Gaussian variable,and d₁ represents the fixed delay during data packet transmission;

The node R returning an ACK message to the node S to be synchronizedafter the timing response interval w_(i), and at the same time,recording a local time T_(3,i) ^((R)) when the ACK message is returned,wherein the interval w_(i) depends on specific conditions of thesequence number of the data packet received by the node R in each cyclemodulo i, and i≥2;

S3: the node S to be synchronized records its local time T_(4,i) ^((S))when receiving the response message from the reference node R; based onthe fact that length of an ACK data packet is usually smaller than thatof a data packet in the network, and that the fixed delay is mainlyinfluenced by the length of the data packet, here, the fixed delay d₂during transmission of an ACK data packet is assume to be equal to thefixed delay d₁ during data packet transmission minus a constant value m,i.e., d₂=d₁−m; similarly, with the influence of the fixed delay d₂during transmission and a random delay Y_(i) in a downlink, thefollowing timestamp relation expression is obtained:

T _(3,i) ^((R)) =α×T _(4,i) ^((S))+θ_(t0)−α×(d ₂ +Y _(i))

wherein Y_(i) is an independent and identically distributed Gaussianvariable;

S4: repeating the above steps S1-S3; if

${\beta = \frac{1}{\alpha}},$

and a matrix is used to store the timestamps T_(1,i) ^((S)), T_(2,i)^((R)), T_(3,i) ^((R)), T_(4,i) ^((S)) and different timing responseintervals w_(i) of the node R, then clock synchronization parameters,i.e., the clock frequency offset α and the fixed time delay d₁ duringdata packet transmission, can be estimated after N cycles, and theformulas are as follows:

$\underset{@R}{\mspace{79mu}\begin{bmatrix}{T_{4,1} - T_{1,1} + m} \\{T_{4,2} - T_{1,2} + m} \\\ldots \\{T_{4,N} - T_{1,N} + m} \\\text{?}\end{bmatrix}} = {{\underset{@M}{\begin{bmatrix}{T_{3,1} - T_{2,1}} & 2 \\{T_{3,2} - T_{2,2}} & 2 \\\ldots & \ldots \\{T_{4,N} - T_{1,N}} & 2 \\\text{?} & \;\end{bmatrix}}\underset{@\Theta}{\begin{bmatrix}\beta \\\text{?}\end{bmatrix}}} + \underset{@Z}{\begin{bmatrix}Z_{1} \\Z_{2} \\\ldots \\\text{?}\end{bmatrix}}}$   Θ̂ = (M^(H)M)⁻¹M^(H)R$\mspace{20mu}{\hat{\alpha} = {\frac{1}{\hat{\beta}} = \frac{1}{\left\lbrack \hat{\Theta} \right\rbrack_{1}}}}$  d̂₁ = [Θ̂]₂ ?indicates text missing or illegible when filed

wherein {circumflex over (α)} is the clock frequency offset estimator,{circumflex over (d)}₁ is the fixed time delay estimator during datapacket transmission, and Z_(i)=X_(i)+Y_(i) is the independent andidentically distributed Gaussian variable, i.e., Z_(i)□N(0,σ²).

Further, in step S2, taking the conditions that the sequence number Seqof the data packet received by the node R in each cycle modulo i withi≥2 as an example, the corresponding rules for obtaining the intervalw_(i) are as follows:

When the sequence number Seq % i=0, the timing response interval forreturning ACK is w₁;

When the sequence number Seq % i=1, the timing response interval forreturning ACK is w₂;

When the sequence number Seq % i=2, the timing response interval forreturning ACK is w₃;

. . . ;

When the sequence number Seq % i=i−2, the timing response interval forreturning ACK is w_(i).

When the sequence number Seq % i=i−1, the timing response interval forreturning ACK is w_(i).

The present invention has following beneficial effects:

(1) The mode of the present invention is based on an ordinary datapacket transmission and ACK communication mechanism, the node to besynchronized can realize the estimation and long-term smooth tracking ofthe clock frequency offset and the fixed delay during the receiving andsending of an ordinary data packet, which saves the energy ofresource-limited sensor nodes and meets the requirement of low powerconsumption of wireless sensor networks.

(2) The method of the present invention does not need dedicatedsynchronization messages with timestamp information for interactionduring the estimation of the clock frequency offset and the fixed delay.In fact, a timestamp is a potential attack point in a timesynchronization protocol, but the method for estimating clock frequencyoffsets provided by the present invention does not need to transmit anytimestamp during implementation, thereby improving the safety of thenetwork.

(3) In the method for estimating clock frequency offsets of industrialwireless sensor networks based on timing response provided by thepresent invention, a time slot template of ISA100.11a is taken as anexample for explanation. The timing response interval for returning ACKdefined by ISA100.11a is expanded, the receiving node adopts thepolicies of establishing a mapping table and conducting modulo operationwith the sequence numbers to obtain two or more different values of thetiming response interval according to different sequence numbers ofreceived data packets, and the timing response intervals for returningACK messages according to different sequence numbers are calculated.Therefore, the present invention is easy to integrate into the existingindustrial wireless sensor networks with a time slot mechanism and has agood practical application value.

DESCRIPTION OF THE DRAWINGS

To enable the purpose, the technical solution and the beneficial effectsof the present invention to be clearer, the present invention providesthe following drawings for explanation:

FIG. 1 is a schematic diagram of a data packet exchange mechanismbetween synchronization nodes of the present invention;

FIG. 2 is a flow chart of a method for estimating clock frequencyoffsets of the present invention;

FIG. 3 is a performance comparison diagram of clock frequency offset andfixed delay estimation results of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Preferred embodiments of the present invention will be described belowin detail in combination with drawings.

FIG. 1 is a schematic diagram of a data packet exchange mechanismbetween synchronization nodes in the method for estimating clockfrequency offsets of industrial wireless sensor networks based on timingresponse of the present invention. As shown in FIG. 1, in an industrialwireless sensor network, an ordinary node S is used as a node to besynchronized, a receiving node R is used as a clock source node, andtwo-way communication between the two nodes is carried out by acommunication mechanism of one-way data packet+ACK.

In the method for estimating clock frequency offsets of industrialwireless sensor networks based on timing response of the presentinvention, because of no timestamp exchange, a synchronization functioncan be embedded in the process of receiving and sending data packets. Itis assumed that the sending node S sends a data packet to the referencenode R at its local time T_(1,i) ^((S)), the reference node R receivesthe data packet after a period of time. After the data packet messagesent by the node S is received, the node R returns an ACK message to thenode S to be synchronized after the timing response interval w_(i), andat the same time, records its local time T_(3,i) ^((R)), when the ACKmessage is returned. The timing response interval w_(i) depends onspecific conditions of the sequence number of the data packet receivedby the node R in each cycle modulo i(i≥2), and the corresponding mappingrules are as follows: when the sequence number Seq % i=0, the timingresponse interval for returning ACK is w₁; when the sequence number Seq% i=1, the timing response interval for returning ACK is w₂; when thesequence number Seq % i=2, the timing response interval for returningACK is w₃; . . . ; when Seq % i=i−2, the timing response interval forreturning ACK is w_(i-1); when Seq % i=i−1, the timing response intervalfor returning ACK is w_(i). Then the node S records the time T_(4,i)^((S)) when receiving the response message. The above process isrepeated, and the clock frequency offset between the nodes and the fixeddelay during data packet transmission can be estimated by a statisticalsignal processing method.

The specific steps are as follows:

For the first synchronization cycle, an implementation model of T_(2,1)^((R)) can be expressed as

T _(2,1) ^((R)) =α×T _(1,1) ^((S))+θ_(t) ₀ +α×(d ₁ +X ₁)  (1)

wherein θ_(t) ₀ and α represent initial clock phase offset and frequencyoffset at time t₀ respectively, and the fixed delay during data packettransmission and random delay in the uplink are respectively denoted byd₁ and X₁.

Here, it is assumed that the sequence number of the first data packetfor data exchange is Seg₀, and Seg₀ is an integer multiple of 3, i.e.,Seg₀%3=0. After a certain interval, the node R returns an ACK message tothe node S. According to the mapping relationship between the sequencenumber of the data packet and the timing response interval, it can beobtained that the timing response interval for returning ACK by the nodeR in the first cycle is w₁.

Assuming that the time when the node R returns ACK is T_(3,1) ^((R)),then:

T _(3,1) ^((R)) =T _(2,1) ^((R)) +w ₁  (2)

The time T_(3,1) ^((R)) when the node R returns ACK and the time T_(4,1)^((S)) when the node S receives ACK satisfy that:

T _(3,1) ^((R)) =α×T _(4,1) ^((S))+θ_(t0)−α×(d ₂ +Y ₁)  (3)

Here, the fixed delay d₂ during transmission of the ACK data packet isequal to the fixed delay d₁ during data packet transmission minus aconstant value m, i.e., d₂=d₁−m, and Y₁ is a random delay in thedownlink of the first cycle.

Similarly, for the second synchronization cycle, T_(2,2) ^((R)) can beexpressed as T_(2,2) ^((R))=α×T_(1,2) ^((S))+θ_(t) ₀ +α×(d₁+X₂), whereinX₂ is the random delay in the uplink in the network during data packettransmission.

When the sequence number of the data packet in the second cycle is thatSeq₁%3=1, it can be obtained that the interval for returning ACK is w₂according to the mapping relationship. The time T_(3,2) ^((R)) when thenode S returns ACK is: T_(3,2) ^((R))=T_(2,2) ^((R))+w₂. T_(3,2) ^((R))and T_(4,2) ^((S)) satisfy the following relationship:

T _(3,2) ^((R)) =α×T _(4,2) ^((S))+θ_(t0)−α×(d ₂ +Y ₂)  (4)

After N rounds of data packet exchange, a mathematical model of theexchange process can be obtained,

T _(2,i) ^((R)) =α×T _(1,i) ^((S))+θ_(t) ₀ −α×(d ₁ +X _(i))  (5)

T _(3,i) ^((R)) =α×T _(4,i) ^((S))+θ_(t0)−α×(d ₂ +Y _(i))  (6)

w _(i)∈(w ₁ ,w ₂ , . . . ,w _(i))  (7)

T _(3,i) ^((R)) =T _(2,i) ^((R)) +w _(i)  (8)

After N cycles, the sending node S can obtain a group of localtimestamps {T_(1,i) ^((S)),T_(4,i) ^((S))}_(i=1) ^(N), and similarly,the node R can obtain a group of local timestamps {T_(2,i) ^((R)),T_(3,i) ^((R))}_(i=1) ^(N). Combined with the different responseintervals w_(i) of the node R, the frequency offset between the nodesand the fixed delay during data packet transmission can be estimated bya statistical signal processing method. The formulas are as follows:

$\begin{matrix}{\underset{@R}{\mspace{79mu}\begin{bmatrix}{T_{4,1} - T_{1,1} + m} \\{T_{4,2} - T_{1,2} + m} \\\ldots \\{T_{4,N} - T_{1,N} + m} \\\text{?}\end{bmatrix}} = {{\underset{@M}{\begin{bmatrix}{T_{3,1} - T_{2,1}} & 2 \\{T_{3,2} - T_{2,2}} & 2 \\\ldots & \ldots \\{T_{4,N} - T_{1,N}} & 2 \\\text{?} & \;\end{bmatrix}}\underset{@\Theta}{\begin{bmatrix}\beta \\\text{?}\end{bmatrix}}} + \underset{@Z}{\begin{bmatrix}Z_{1} \\Z_{2} \\\ldots \\\text{?}\end{bmatrix}}}} & (9) \\{\mspace{79mu}{{\hat{\Theta} = {\left( {M^{H}M} \right)^{- 1}M^{H}R}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (10)\end{matrix}$

Thus, a clock frequency offset estimator {circumflex over (α)} of thesending node S relative to the node R and a fixed time delay estimator{circumflex over (d)}₁ during data packet transmission can be obtained,wherein Z_(i)=X_(i)+Y_(i) is the independent and identically distributedGaussian variable, i.e., Z_(i)□N(0, σ²), and N is the number ofsynchronization cycles between the two nodes.

$\begin{matrix}{\hat{\alpha} = {\frac{1}{\hat{\beta}} = \frac{1}{\left\lbrack \hat{\Theta} \right\rbrack_{1}}}} & (11) \\{{\hat{d}}_{1} = \left\lbrack \hat{\Theta} \right\rbrack_{2}} & (12)\end{matrix}$

In order to verify the effectiveness of the method for estimating clockfrequency offsets of industrial wireless sensor networks based on timingresponse provided by the present invention, a Cramer-Rao Lower Bound(CRLB) is calculated.

$\begin{matrix}{{{Var}\left( \hat{\beta} \right)} \geq \frac{N\sigma^{2}}{\begin{matrix}{{N\;\alpha^{2}{\sum\limits_{i = 1}^{N}\left\lbrack {\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)^{2} + \delta^{2}} \right\rbrack}} -} \\{\alpha^{2}\left\lbrack {\sum\limits_{i = 1}^{N}\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)} \right\rbrack}^{2}\end{matrix}}} & (13) \\{{{Var}\left( {\hat{d}}_{1} \right)} \geq \frac{\sigma^{2}{\sum\limits_{i = 1}^{N}\left\lbrack {\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)^{2} + \delta^{2}} \right\rbrack}}{\begin{matrix}{{4N{\sum\limits_{i = 1}^{N}\left\lbrack {\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)^{2} + \delta^{2}} \right\rbrack}} -} \\{4\left\lbrack {\sum\limits_{i = 1}^{N}\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)} \right\rbrack}^{2}\end{matrix}}} & (14)\end{matrix}$

Here, β is the inverse of the frequency offset α to be estimated, i.e.,

${\alpha = \frac{1}{\beta}},$

and d₁ is the fixed delay during data packet transmission. The CRLB of amore general function α=g(β) of β can be obtained according to parametertransformation when the CRLB of β

is known. The specific transformation formula is as follows:

$\begin{matrix}{{{Var}\left( \hat{\alpha} \right)} \geq {\left( \frac{\partial g}{\partial\beta} \right)^{2}{{Var}\left( \hat{\beta} \right)}}} & (15)\end{matrix}$

Thus, the CRLB of the frequency offset α is:

$\begin{matrix}{{{Var}\left( \hat{\alpha} \right)} \geq {\left( {- \frac{1}{\beta}} \right)^{2}{{Var}\left( \hat{\beta} \right)}} \geq \frac{N\sigma^{2}\alpha^{2}}{\begin{matrix}{{N{\sum\limits_{i = 1}^{N}\left\lbrack {\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)^{2} + \delta^{2}} \right\rbrack}} -} \\\left\lbrack {\sum\limits_{i = 1}^{N}\left( {T_{4,i} - T_{1,i} - {2d_{1}} + m} \right)} \right\rbrack^{2}\end{matrix}}} & (16)\end{matrix}$

Embodiment

FIG. 2 is a flow chart of a method for estimating clock frequencyoffsets based on timing response of the present invention. As shown inFIG. 2, the method for estimating clock frequency offsets specificallycomprises the following steps:

S1: starting a synchronization process.

S2: a sending node S sending a data packet with a sequence number of Seqto a receiving node R, and recording a sending time T_(1,i) ^((S)).

S3: the receiving node R receiving the data packet, and recording areceiving time T_(2,i) ^((R)).

S4: the receiving node R obtaining a timing response interval w_(i)required to wait for returning ACK according to the sequence number ofthe received data packet by a calculation rule Seq % i.

S5: the receiving node R returning an ACK response after the intervalw_(i), and recording a corresponding sending time T_(3,i) ^((R)).

S6: the node S receiving the response ACK message from the node R, andrecording a corresponding receiving time T_(4,i) ^((S)).

S7-S9: determining whether the number of synchronization cycles reachesa set value N; if yes, estimating the frequency offset and the fixeddelay between the nodes; otherwise, i=i+1, entering step S2 andcontinuing to repeat the data packet sending and receiving process.

S10: the node S to be synchronized estimating clock synchronizationparameters, i.e., the frequency offset and the fixed delay, which lays afoundation for time synchronization of an industrial wireless sensornetwork.

S11: ending the synchronization process.

FIG. 3 is a performance comparison diagram of clock frequency offset andfixed time delay estimation results obtained by the method forestimating clock frequency offsets of the present invention comparedwith corresponding CRLBs. It can be known from FIG. 3 that mean squareerrors of both estimators are reduced with the increase of the number ofobservations; each mean square error curve is roughly coincident withthe corresponding CRLB thereof, the effectiveness of the estimators{circumflex over (α)} and {circumflex over (d)}₁ are verified bysimulation results, and the estimated performance is close to optimalestimate.

Finally, it should be noted that the above preferred embodiments areonly used for describing, rather than limiting the technical solution ofthe present invention. Although the present invention is alreadydescribed in detail through the above preferred embodiments, thoseskilled in the art shall understand that various changes in form anddetail can be made to the present invention without departing from thescope defined by claims of the present invention.

1. A method for estimating clock frequency offsets of industrialwireless sensor networks based on timing response, characterized inthat: in a wireless sensor network, when an arbitrary node S to besynchronized in the network need to realize synchronization with areference node R, two-way communication between the nodes is carried outin a communication mode of one-way data packet+ACK, and estimation oftime synchronization parameters does not depend on exchange of a lot oftimestamp information; because no timestamp exchange is required,synchronization function can be embedded into an existing data exchangeprocess; after a data packet message sent by a sending node S isreceived by the reference node R, two or more different values of atiming response interval are obtained according to a sequence number(Seq) of a received data packet by adopting corresponding rules; and themethod specifically comprises the following steps: S1: estimation of aclock frequency offset is performed along with data packet sending andreceiving of the nodes, assuming that the node S to be synchronizedsends a data packet to the reference node R at a local time T_(1,i)^((S)), and records the sending time T_(1,i) ^((S)); S2: as crystaloscillators of the node R and the node S have different frequencies, iff_(R) represents a crystal oscillator frequency of the node R, and f_(S)represents a crystal oscillator frequency of the node S, the referencenode R records a local time T_(2,i) ^((R)) when receiving a data framesent by the node S; as influenced by a fixed delay d₁ during data packettransmission and a random delay X_(i) in an uplink, it can be obtainedthatT _(2,i) ^((R)) =α×T _(1,i) ^((S))+θ_(t0)+α×(d ₁ +X _(i)) wherein$\alpha = \frac{f_{R}}{f_{S}}$ represents a clock frequency offset ofthe node S relative to the node R, θ_(t) ₀ represents an initial phaseoffset between the nodes, X_(i) represents an independent andidentically distributed Gaussian variable, and d₁ represents the fixeddelay during data packet transmission; the node R returning an ACKmessage to the node S to be synchronized after the timing responseinterval w_(i), and records a local time T_(3,i) ^((R)) when the ACKmessage is returned, wherein the interval w_(i), is obtained accordingto the sequence number of the data packet received by the node R in eachcycle and the corresponding rules for timing response; S3: the node S tobe synchronized records a local time T_(4,i) ^((S)) when receiving aresponse message from the reference node R; assuming that a fixed delayd₂ during transmission of an ACK data packet is equal to the fixed timedelay d₁ during data packet transmission minus a constant value m, i.e.,d₂=d₁−m; similarly, with the influence of the fixed time delay d₂ duringtransmission and a random delay Y_(i) in a downlink, the followingtimestamp relational expression is obtained:T _(3,i) ^((R)) =α×T _(4,i) ^((S))+θ_(t0)−α×(d ₂ +Y _(i)) wherein Y_(i)is an independent and identically distributed Gaussian variable; S4:repeating the above steps S1-S3; if ${\beta = \frac{1}{\alpha}},$ and amatrix is used to store the timestamps T_(1,i) ^((S)), T_(2,i) ^((R)),T_(3,i) ^((R)), T_(4,i) ^((S)) and different timing response intervalsw_(i) of the node R, then clock synchronization parameters, i.e., theclock frequency offset α and the fixed time delay d₁ during data packettransmission, can be estimated after N cycles, and the formulas are asfollows: $\underset{@R}{\mspace{79mu}\begin{bmatrix}{T_{4,1} - T_{1,1} + m} \\{T_{4,2} - T_{1,2} + m} \\\ldots \\{T_{4,N} - T_{1,N} + m} \\\text{?}\end{bmatrix}} = {{\underset{@M}{\begin{bmatrix}{T_{3,1} - T_{2,1}} & 2 \\{T_{3,2} - T_{2,2}} & 2 \\\ldots & \ldots \\{T_{4,N} - T_{1,N}} & 2 \\\text{?} & \;\end{bmatrix}}\underset{@\Theta}{\begin{bmatrix}\beta \\\text{?}\end{bmatrix}}} + \underset{@Z}{\begin{bmatrix}Z_{1} \\Z_{2} \\\ldots \\\text{?}\end{bmatrix}}}$   Θ̂ = (M^(H)M)⁻¹M^(H)R$\mspace{20mu}{\hat{\alpha} = {\frac{1}{\hat{\beta}} = \frac{1}{\left\lbrack \hat{\Theta} \right\rbrack_{1}}}}$  d̂₁ = [Θ̂]₂ ?indicates text missing or illegible when filed wherein{circumflex over (α)} is a clock frequency offset estimator, {circumflexover (d)}₁ is a fixed delay estimator during data packet transmission,and Z_(i)=X_(i)+Y_(i) is the independent and identically distributedGaussian variable, i.e., Z_(i)□N(0, δ²).
 2. The method for estimatingclock frequency offsets of industrial wireless sensor networks based ontiming response as claimed in claim 1, characterized in that: in stepS2, two or more different values of the interval w_(i) are obtainedaccording to the corresponding rules; in the conditions of the sequencenumber Seq of the data packet received by the node R in each cyclemodulo i with i≥2, the corresponding rules are as follows: when thesequence number Seq % i=0, the timing response interval for returningACK is w₁; when the sequence number Seq % i=1, the timing responseinterval for returning ACK is w₂; when the sequence number Seq % i=2,the timing response interval for returning ACK is w₃; . . . ; when thesequence number Seq % i=i=2, the timing response interval for returningACK is w_(i-1); when the sequence number Seq % i=i−1, the timingresponse interval for returning ACK is w_(i).